Transformations

Reflections Lines of symmetry do not always have to touch the object Image Mirror line

Object Image Mirror line

Copy these axes on to squared paper Plot these points A(1, 2), B(2, 4) C(5, 1) A2 B2 C2 B Join the points to get triangle ABC A C Reflect triangle ABC in the x-axis to get a new triangle A1B1C1 A1 B1 C1 A3 B3 C3 Reflect triangle ABC in the y-axis to get a new triangle A2B2C2 Reflect triangle ABC in the y = -x to get a new triangle A3B3C3

Translations A translation can be thought as a sliding movement Translate the triangle 4 squares to the right 4 squares

Translate the triangle 3 squares upwards

Translate the triangle 4 squares to the right and 3 squares upwards This is written as Movement right or left 3 squares Translation 4 squares Movement up or down

For translating the triangle 4 squares to the right and 3 squares upwards the movement can be thought as like this Translation

For translating the triangle 3 squares to the left and 4 squares downwards the movement can be thought as like this This is written as Translation

Rotations In a rotation an object is turned about a point through an angle. The point is called the centre of rotation. Anticlockwise rotations are positive and clockwise are negative Rotate triangle ABC about O through to get a new triangle A1B1C1 A B C A1 B1 C1 O Centre of rotation

The centre of rotation can be in different places Rotate triangle ABC about O through to get a new triangle A1B1C1 A1 B1 C1 Centre of rotation O

Enlargement An enlargement changes the size of an object. The change is the same in all directions Enlarge the rectangle by a scale factor of 2 6 squares 4 squares 3 squares 2 squares

Enlargements are normally done from a centre of enlargement. Enlarge the triangle ABC by a scale factor 2. Use O as the centre of enlargement. Measure the distance from the centre O to the vertex A on the triangle C1 A B C Then multiply this distance by the scale factor. Label this point A1 B1 A1 Repeat for the other vertices B and C O

The centre of enlargement does not always have to be in the same place Enlarge the triangle ABC by a scale factor 3. Use O as the centre of enlargement. A B C O A1 B1

The scale factor can also be less than 1 Enlarge the triangle ABC by a scale factor . Use O as the centre of enlargement. A B C C1 B1 A1 O

The scale factor can also be less than 0 Enlarge the triangle ABC by a scale factor -2. Use O as the centre of enlargement. A1 O Notice that the image A1B1C1 is inverted B1 C1

To find the mirror line of a reflection given the object and its image Join two corresponding points on the object and its image AA1 A1 B1 C1 A B C Construct the perpendicular bisector of this line segment Perpendicular bisector of AA1 i.e. mirror line

To find the centre of rotation given an object and its image Join two corresponding points on the object and its image AA1 A B C Draw the perpendicular bisector of this line segment A1 B1 C1 Repeat for two other corresponding points BB1 Centre of rotation